A deadlock is a state of a system in which no single process/thread is capable of executing an action. As mentioned by others, a deadlock is typically the result of a situation where each process/thread wishes to acquire a lock to a resource that is already locked by another (or even the same) process/thread.
There are various methods to find them and avoid them. One is thinking very hard and/or trying lots of things. However, dealing with parallelism is notoriously difficult and most (if not all) people will not be able to completely avoid problems.
Some more formal methods can be useful if you are serious about dealing with these kinds of issues. The most practical method that I'm aware of is to use the process theoretic approach. Here you model your system in some process language (e.g. CCS, CSP, ACP, mCRL2, LOTOS) and use the available tools to (model-)check for deadlocks (and perhaps some other properties as well). Examples of toolset to use are FDR, mCRL2, CADP and Uppaal. Some brave souls might even prove their systems deadlock free by using purely symbolic methods (theorem proving; look for Owicki-Gries).
However, these formal methods typically do require some effort (e.g. learning the basics of process theory). But I guess that's simply a consequence of the fact that these problems are hard.